Write Down the Transition Matrix Associated with the Given State $$A = B = C = \frac { 1 } { 3 }$$

Multiple Choice

Write down the transition matrix associated with the given state transition diagram. $$A = B = C = \frac { 1 } { 3 }$$ , $$D = E = H = \frac { 2 } { 3 }$$

A) $P = \left[ \begin{array} { c c c c c } 1 & 0 & 0 & 0 & 0 \\\frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } & 0 & 0 \\0 & \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } & 0 \\0 & 0 & \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } \\0 & 0 & 0 & 0 & 1\end{array} \right]$
B) $P = \left[ \begin{array} { c c c c c } 1 & 0 & 0 & 0 & 0 \\\frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } & 0 & 0 \\0 & \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } & 0 \\0 & 0 & \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } \\0 & 0 & 0 & 1 & 0\end{array} \right]$
C) $P = \left[ \begin{array} { c c c c c } 1 & 0 & 0 & 0 & 0 \\\frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 & 0 \\0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 \\0 & 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } \\0 & 0 & 0 & 1 & 0\end{array} \right]$
D) $P = \left[ \begin{array} { c c c c c } 0 & 1 & 0 & 0 & 0 \\\frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 & 0 \\0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 \\0 & 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } \\0 & 0 & 0 & 1 & 0\end{array} \right]$
E) $P = \left[ \begin{array} { c c c c c } 1 & 0 & 0 & 0 & 0 \\\frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 & 0 \\0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 \\0 & 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } \\0 & 0 & 0 & 0 & 1\end{array} \right]$